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" AC 2AC nearly ; that is, the difference between the true and apparent level is equal to the square of the distance between the places, divided by the diameter of the earth ; and consequently it is always proportional to the square of the distance. "
A Treatise on the Principal Mathematical Instruments Employed in Surveying ... - Page 28
by Frederick Walter Simms - 1834 - 100 pages
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 2

1801 - 658 pages
...sensible AB * AT\ * error ; 2OD XDB= A1V, or DB = -— = -^~ aOD aOD nearly. That That is, the difference between the true and apparent level is equal to the...always proportional to the square of the distance. Now suppose, for example, we want to know the difference between the true and apparent level at the distance...
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Recreations in Mathematics and Natural Philosophy ...

Jacques Ozanam - 1803 - 660 pages
...of the arch of distance above the radius of the earth. Hence it will be found that this difference is equal to the square of the distance between the...always proportional to the square of the distance. From these principles is obtained the following table, which shews the height of the apparent above...
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Comprehensive treatise on land surveying

John Ainslie - 1812 - 358 pages
...those tables are constructed, but shall merely give the following position, vix. That the difference between the true and apparent level is equal to the square of the distance between the two places or stations divided by the earth's diameter, and consequently is always proportional...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - 666 pages
...true and apparent level, at any distance, may be found by a well-known property of the circle, to be equal to the square of the distance between the places,...distance. Now the diameter of the earth being nearly 7958 miles, if we first take the distance = 1 mile, then the excess becomes 7,962 inches, or almost...
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An encyclopædia of agriculture

John Claudius Loudon - 1825 - 1250 pages
...like, the difference between the true and the apparent level must be taken into the account, which is equal to the square of the distance between the...always proportional to the square of the distance ; or from calculation almost eight inches, for the height of the apparent above tile true level at...
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A Dictionary of Mechanical Science, Arts, Manufactures, and ..., Volume 2

Alexander Jamieson - 1829 - 654 pages
...2A С : BD :: BD : CD, which therefore is = - — ,- — 2 AC 2AC nearly ; that is, the difference between the true and apparent level is equal to the...distance. Now the diameter of the earth being nearly 7958 miles, if we в с' first take В С = 1 mile, then the excess rr — — becomes .¿¡g of *í...
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Recreations in mathematics and natural philosophy, recomposed by m. Montucla ...

Jacques Ozanam - 1840 - 850 pages
...of the arch of distance above the radius of the earth. Hence it will be found that this difference is equal to the square of the distance between the...always proportional to the square of the distance. From these principles is obtained the following table, which shews the height of the apparent above...
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Crocker's Elements of land surveying. To which are added, Tables of six ...

Abraham Crocker - 1841 - 486 pages
...2AC : BD : : BD ; CD, which therefore is = BT)2 TIP 2 SAP' °r 2AC nearty' *hat 's> *^e difference between the true and apparent level is equal to the...always proportional to the square of the distance. 278 LAND-MEASURING. The diameter of the earth being nearly 7958 miles ; EC2 if we first take BC = 1...
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A Treatise on Military Surveying: Including Sketching in the Field, Plan ...

Basil Jackson - 1847 - 410 pages
...as equal to AB. Then, 2CH: AB::AB:HB; or =£' very nearly. By which it appears, that the difference between the true and apparent level is equal to the square of the distance between the stations, divided by the diameter of the globe. It is, therefore, always proportional to the square...
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Instructions in Practical Surveying, Topographical Plan-drawing, and ...

George D. Burr - 1847 - 270 pages
...sensible error, and it becomes 2AC:BD::BD:CD, or - - = - very nearly. Hence the difference 2 AC 2 AC between the true and apparent level is equal to the square of the distance between the stations divided by the diameter of the earth, and, therefore, is always proportional to the square...
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